Project Summary Application of Computational Fluid Dynamics (CFD) to the flow analysis and design of complex medical devices such as prosthetic heart valves and ventricular assist devices is by now standard practice in the medical devices research and development community. However, a recent controlled study by the FDA has demonstrated the limitations of traditional CFD in predicting laminar-transitional-turbulent flows of relevance to cardiovascular devices. In particular, no statistical turbulence model used in the medical devices community benchmarked uniformly successfully against experimental data. Large Eddy Simulation (LES) was recommended in this study for future simulations. To address the recommendation of the FDA panel to use LES in future simulations we propose to develop an advanced new-generation CFD for low-Reynolds-number turbulent flows of relevance to the NIH mission, using (1) a high-order Eulerian vorticity transport method for LES in the boundary layer region, and Direct Numerical Simulation (DNS) in the immediate vicinity of the boundary; and (2) an existing meshless Lagrangian Vortex Method (LVM) for LES of the large scale flow away from the boundary layer. The velocity evaluations, which constitute roughly 80% of the computational cost, will be parallelized on multicore CPUs and multi-GPUs. The Specific Aims of the project are: Specific Aim 1: To develop a compact high-order finite volume method for laminar flow simulation via the vorticity transport equation (VTE); to accelerate the velocity evaluations on multicore CPUs and multi-GPUs; and to rigorously validate the laminar flow code using, among others, the FDA Critical Path problem #1 (nozzle), as well as DNS of steady and pulsatile stenotic flow. Specific Aim 2: To develop a dynamic Subgrid-Scale (SGS) model in the context of VTE and tailored for transitional flow; and to validate the high-order finite volume code for turbulent flow using, among others, the FDA Critical Path problem #1 (nozzle), as well as steady and pulsatile stenotic flow. Specific Aim 3: To finalize the development of the proposed hybrid code for LES of low-Reynolds-number turbulent flow by coupling the high-order Eulerian and Lagrangian vortex element solvers, accurately and stably; and to validate the final product using a series of benchmarks, including the FDA Critical Path problems #1 (nozzle) and #2 (pump), as well as an actual blood pump; e.g., the HeartMate II. Specific Aim 4: To implement a system for successful documentation, dissemination, and maintenance of the software, and to accommodate collaborative research; and to develop interfaces to mainstream CFD to ensure interoperability and seamless migration to the propsed technology. Long-Term Impact: At present, application of traditional CFD and statistical turbulence models is limited to the study of device performance in terms of relative trends. That is, CFD is not yet a truly predictive design and analysis tool, at least in the case of cardio-device design, which involves highly complex unsteady flow with multiple coexisting laminar, transitional, and turbulent flow regimes. The proposed high-order hybrid DNS-LES method is designed to be a predictive tool that avoids ad hoc model constants especially within the boundary layer, which is a key source of shear stress and blood damage. The proposed technology will fundamentally alter how the medical devices community will use CFD in future. The long-term significant impact of this research and technology maturation project is a CFD software that (1) is incredibly easy to learn and use, as it obviates the often tedious and error prone volumetric meshing process; (2) can be used reliably as a predictive tool thanks to the absence of turbulence models with ad hoc fudge factors, which must invariably be calibrated and validated for each new flow problem; and (3) can be run on a desktop at order-of-magnitude faster turn-around times, reducing month-long product design cycles to just days, thanks to advanced algorithms and accelerated computing on commodity multicore CPUs and multi-GPUs.